time-to-botec

Benchmark sampling in different programming languages
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README.md (4057B)

      1 <!--
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      3 @license Apache-2.0
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      5 Copyright (c) 2018 The Stdlib Authors.
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      7 Licensed under the Apache License, Version 2.0 (the "License");
      8 you may not use this file except in compliance with the License.
      9 You may obtain a copy of the License at
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     11    http://www.apache.org/licenses/LICENSE-2.0
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     13 Unless required by applicable law or agreed to in writing, software
     14 distributed under the License is distributed on an "AS IS" BASIS,
     15 WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
     16 See the License for the specific language governing permissions and
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     19 -->
     20 
     21 # Skewness
     22 
     23 > [Gamma][gamma-distribution] distribution [skewness][skewness].
     24 
     25 <!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
     26 
     27 <section class="intro">
     28 
     29 The [skewness][skewness] for a [gamma][gamma-distribution] random variable with shape parameter `α > 0` and rate parameter `β > 0` is
     30 
     31 <!-- <equation class="equation" label="eq:gamma_skewness" align="center" raw="\operatorname{skew}\left( X \right) = \frac{2}{\sqrt{\alpha}}" alt="Skewness for a gamma distribution."> -->
     32 
     33 <div class="equation" align="center" data-raw-text="\operatorname{skew}\left( X \right) = \frac{2}{\sqrt{\alpha}}" data-equation="eq:gamma_skewness">
     34     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/gamma/skewness/docs/img/equation_gamma_skewness.svg" alt="Skewness for a gamma distribution.">
     35     <br>
     36 </div>
     37 
     38 <!-- </equation> -->
     39 
     40 </section>
     41 
     42 <!-- /.intro -->
     43 
     44 <!-- Package usage documentation. -->
     45 
     46 <section class="usage">
     47 
     48 ## Usage
     49 
     50 ```javascript
     51 var skewness = require( '@stdlib/stats/base/dists/gamma/skewness' );
     52 ```
     53 
     54 #### skewness( alpha, beta )
     55 
     56 Returns the [skewness][skewness] of a [gamma][gamma-distribution] distribution with parameters `alpha` (shape parameter) and `beta` (rate parameter).
     57 
     58 ```javascript
     59 var v = skewness( 1.0, 1.0 );
     60 // returns 2.0
     61 
     62 v = skewness( 4.0, 12.0 );
     63 // returns 1.0
     64 
     65 v = skewness( 8.0, 2.0 );
     66 // returns ~0.707
     67 ```
     68 
     69 If provided `NaN` as any argument, the function returns `NaN`.
     70 
     71 ```javascript
     72 var v = skewness( NaN, 2.0 );
     73 // returns NaN
     74 
     75 v = skewness( 2.0, NaN );
     76 // returns NaN
     77 ```
     78 
     79 If provided `alpha <= 0`, the function returns `NaN`.
     80 
     81 ```javascript
     82 var v = skewness( 0.0, 1.0 );
     83 // returns NaN
     84 
     85 v = skewness( -1.0, 1.0 );
     86 // returns NaN
     87 ```
     88 
     89 If provided `beta <= 0`, the function returns `NaN`.
     90 
     91 ```javascript
     92 var v = skewness( 1.0, 0.0 );
     93 // returns NaN
     94 
     95 v = skewness( 1.0, -1.0 );
     96 // returns NaN
     97 ```
     98 
     99 </section>
    100 
    101 <!-- /.usage -->
    102 
    103 <!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
    104 
    105 <section class="notes">
    106 
    107 </section>
    108 
    109 <!-- /.notes -->
    110 
    111 <!-- Package usage examples. -->
    112 
    113 <section class="examples">
    114 
    115 ## Examples
    116 
    117 <!-- eslint no-undef: "error" -->
    118 
    119 ```javascript
    120 var randu = require( '@stdlib/random/base/randu' );
    121 var EPS = require( '@stdlib/constants/float64/eps' );
    122 var skewness = require( '@stdlib/stats/base/dists/gamma/skewness' );
    123 
    124 var alpha;
    125 var beta;
    126 var v;
    127 var i;
    128 
    129 for ( i = 0; i < 10; i++ ) {
    130     alpha = ( randu()*10.0 ) + EPS;
    131     beta = ( randu()*10.0 ) + EPS;
    132     v = skewness( alpha, beta );
    133     console.log( 'α: %d, β: %d, skew(X;α,β): %d', alpha.toFixed( 4 ), beta.toFixed( 4 ), v.toFixed( 4 ) );
    134 }
    135 ```
    136 
    137 </section>
    138 
    139 <!-- /.examples -->
    140 
    141 <!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
    142 
    143 <section class="references">
    144 
    145 </section>
    146 
    147 <!-- /.references -->
    148 
    149 <!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
    150 
    151 <section class="links">
    152 
    153 [gamma-distribution]: https://en.wikipedia.org/wiki/Gamma_distribution
    154 
    155 [skewness]: https://en.wikipedia.org/wiki/Skewness
    156 
    157 </section>
    158 
    159 <!-- /.links -->